Virtual model of articulation from intra-oral scans

ABSTRACT

A method for determining virtual articulation from dental scans. The method includes receiving digital 3D models of a person&#39;s maxillary and mandibular arches, and digital 3D models of a plurality of different bite poses of the arches. The digital 3D models of the maxillary and mandibular arches are registered with the bite poses to generate transforms defining spatial relationships between the arches for the bite poses. Based upon the digital 3D models and transforms, the method computes a pure rotation axis representation for each bite pose of the mandibular arch with respect to the maxillary arch. The virtual articulation can be used in making restorations or for diagnostic purposes.

BACKGROUND

Digital dentistry is a growing trend with an increasing number ofdentists relying on digital impressioning systems. These systems use anintra-oral scanning camera, or scanning of a traditional physicalimpression, and an associated processing system to generate a digitalthree-dimensional (3D) model of patients' teeth.

The digital 3D models can then be used to make prosthodonticrestorations and for advanced diagnostics such as detecting tooth wear.Accurate articulation is a key factor in making such restorations andfor the diagnostics. Current data acquisition for mechanicalarticulation is time consuming and requires expensive analog devices. Inparticular, the current technique involves a manual process using a facebow and lab articulator to capture mandibular articulation data forcomplex rehabilitations.

Accordingly, a need exists for a digital replacement to the currentmanual process for obtaining articulation information.

SUMMARY

A method for determining virtual articulation from dental scans,consistent with the present invention, includes receiving digital 3Dmodels of a person's maxillary and mandibular arches, and receivingdigital 3D models of a plurality of different bite poses of themaxillary and mandibular arches. The method determines a virtualarticulation model, based upon the digital 3D models of the plurality ofdifferent bite poses, including a digital representation of a purerotation axis of the mandibular arch with respect to the maxillary archfor each articulation motion corresponding to a bite pose.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings are incorporated in and constitute a part ofthis specification and, together with the description, explain theadvantages and principles of the invention. In the drawings,

FIG. 1 is a diagram of a system for generating virtual articulationusing digital 3D models from intra-oral scans;

FIG. 2 illustrates a 3D model of teeth from intra-oral scans;

FIG. 3 is a flow chart representing determination of virtualarticulation from intra-oral scans;

FIG. 4 illustrates bite poses for scans to generate virtualarticulation;

FIG. 5 illustrates registering the scans of bite poses to a referencescan;

FIG. 6 illustrates converting a translation vector with a rotationcomponent to a pure rotation axis;

FIG. 7 illustrates a digital 3D model illustrating articulation motionsin a virtual model;

FIG. 8 illustrates a digital 3D model of a maxillary arch;

FIG. 9 illustrates a digital 3D model of a mandibular arch;

FIG. 10 illustrates a digital 3D model of a closed bite pose;

FIG. 11 illustrates a digital 3D model of an open bite pose;

FIG. 12 illustrates a digital 3D model of a protrusive (forward) bitepose;

FIG. 13 illustrates a digital 3D model of a left lateral bite pose;

FIG. 14 illustrates a digital 3D model of a right lateral bite pose;

FIG. 15 illustrates a digital 3D model of an open pose;

FIG. 16 illustrates a digital 3D model of a protrusive pose;

FIG. 17 illustrates a digital 3D model of a left lateral pose;

FIG. 18 illustrates a digital 3D model of a right lateral pose;

FIG. 19 illustrates an original rotation axis in a digital 3D model;

FIG. 20 illustrates a translation vector in a digital 3D model;

FIG. 21 illustrates rotation and translation vectors;

FIG. 22 illustrates a vectorial composition;

FIG. 23 illustrates vectors with a digital 3D model;

FIG. 24 illustrates vectors with a digital 3D model;

FIG. 25 illustrates a digital 3D model with four different axes whichanimate the mandible model for virtual articulation; and

FIG. 26 is a diagram of a user interface for applying a virtualarticulation model.

DETAILED DESCRIPTION

The use of digital 3D models in the dental market is becoming moreprevalent. These models can either be acquired directly in vivo using anintra-oral scanner, Cone Beam Computed Tomography (CBCT) scanning (i.e.,3D X-ray), or Magnetic Resonance Imaging (MRI), for example; or they canbe acquired indirectly by scanning an impression of the teeth or acasting made from an impression of the teeth. Some examples of indirectdata acquisition methods include, but are not limited to, industrialComputed Tomography (CT) scanning (i.e., 3D X-ray), laser scanning, andpatterned light scanning. The digital 3D models can be used for variedclinical tasks including treatment planning, crown and implantpreparation, prosthodontic restorations, orthodontic setup design,orthodontic appliance design, and in diagnostic aides, for example toassess or visually illustrate tooth wear.

Overview

Embodiments of the present invention calculate a virtual model ofmandibular articulation from several extreme bite scans captured with anintraoral scanner. Since the virtual model permits reproducing anypossible movement of the patient's mandible relative to the maxilla,this invention can facilitate, for example, prosthesis design,orthodontic setup design, wear facets identification, facets root causeidentification, tooth wear prediction, dynamic occlusion design andadjustment (lateral and protrusive interferences avoidance, prematurecontacts elimination) and other advanced diagnoses, predictions andtreatment plans. A key innovation is the calculation of mandibularmotion from tooth surface data available via intra-oral scanners.

FIG. 1 is a diagram of a system 10 for generating virtual articulationusing digital 3D models from intra-oral scans. System 10 includes aprocessor 20 receiving digital 3D models of teeth or other intra-oralstructures (12) from intra-oral 3D scans or scans of impressions orcastings of teeth. System 10 can also include an electronic displaydevice 16 for displaying digital 3D models from scans of intra-oralstructures and an input device 18 for receiving user commands or otherinformation. An example of a digital 3D model of a patient's teeth froma scan is shown in FIG. 2. Systems to generate digital 3D images ormodels based upon image sets from multiple views are disclosed in U.S.Pat. Nos. 7,956,862 and 7,605,817, both of which are incorporated hereinby reference as if fully set forth. These systems can use an intra-oralscanner to obtain digital images from multiple views of teeth or otherintra-oral structures, and those digital images are processed togenerate a digital 3D model or scan representing the scanned teeth orother intra-oral structure. The 3D models or scans can be implementedas, for example, a polygonal mesh or point cloud representing thesurface of the scanned object or intra-oral structure.

Intra-oral structures include dentition, and more typically humandentition, such as individual teeth, quadrants, full arches, pairs ofarches which may be separate or in occlusion of various types, softtissue (e.g., gingival and mucosal surfaces of the mouth, or perioralstructures such as the lips, nose, cheeks, and chin), and the like, aswell as bones and any other supporting or surrounding structures.Intra-oral structures can possibly include both natural structureswithin a mouth and artificial structures such as dental objects (e.g.,prosthesis, implant, appliance, restoration, restorative component, orabutment).

System 10 can be implemented with, for example, a desktop, notebook, ortablet computer. System 10 can receive the 3D scans locally or remotelyvia a network. Display device 16 can be implemented with any electronicdisplay, for example a Cathode Ray Tube (CRT), a liquid crystal display(LCD), light emitting diode (LED) display, or organic light emittingdiode (OLED) display. Input device 18 can be implemented with any devicefor entering information or commands, for example a keyboard,microphone, cursor-control device, or touch screen. The components ofsystem 10 may also be combined, e.g., a tablet computer can incorporatethe processor, display and touch screen input devices into a singleunit.

FIG. 3 is a flow chart representing a method for determining virtualarticulation from intra-oral scans. This method includes, as furtherexplained below, receiving digital 3D models or scans 1-n (step 22),determining articulation from the scans including protrusive (andoptionally retrusive), open, lateral left, and lateral right purerotation axes (step 24), outputting a virtual articulation modelrepresenting the movement of a person's mandible (step 26), anddisplaying a pose of the virtual articulation model based upon userinput for the pure rotation axes or other types of input (step 28). Thestep 24 for determining articulation includes, as further explainedbelow, registering scans of bite poses with a reference scan (step 23),determining translation vectors and original rotation axes (step 25),and determining pure rotation axes from the translation vectors andoriginal rotation axes (step 27). This method can be implemented insoftware or firmware modules for execution by a processor such asprocessor 20, and the method can possibly be implemented using cloudcomputing. The virtual articulation model can be displayed on a displaydevice such as display device 16, and a user may interact with thevirtual articulation model via display device 16 and input device 18.

The inputs to the method are a mandible scan, maxilla scan, and thefollowing five bite pose scans: closed (centric/maximum intercuspation);open; forward or protrusive (and optionally retrusive); lateral left;and lateral right. FIG. 4 illustrates these bite poses of a mandibular(lower) arch 31 position with respect to a maxillary (upper) arch 30.The method finds the best fit registrations of these mandibular andmaxillary arches to each of the five bite scans, establishing therelative relationship between the mandible and maxilla for each. FIG. 5illustrates registering the scans of bite poses to a reference scan. Inparticular, and in this example, a closed bite scan 32, correspondingwith a scan of maxillary and mandibular arches 30 and 31 in the closedposition, is used as the reference scan, and the scans of the bitepositions, right scan 33, forward scan 34, open scan 35, and left scan36, are each registered with closed scan 32. Aside from closed scan 32,other scans can be used as the reference scan for the registration.

Using the maxilla as a fixed reference coordinate system, the methodtransforms these relative relationships into a shared coordinate systemto attain transforms describing the extreme mandibular pose for eachindividual type of articulation relative to the closed pose, inparticular closed to open, closed to protrusive, closed to lateral left,and closed to lateral right. Various forms of interpolation of themandible position and orientation between the closed and respective bitepose, reflecting the mandible motion to attain that specific pose, arethen possible. The overall mandibular motion in the virtual articulationmodel can then be expressed as composite transforms of the fourindividual articulation transforms at various stages of interpolation,limiting the interpolations according to physical anatomicalconstraints. Aside from extreme mandibular poses to the limits of thosepose positions, other mandibular poses having a significantdisplacement, or at least sufficient displacement, to generate thevirtual articulation can be used.

The movement of the mandible from the closed pose to any of the otherposes can be described, for each pose, as the combination of a rotationmatrix (the composite of three rotations around the coordinate axes x,y, z) and a translation vector of the origin of coordinates. Thiscombination (rotation plus translation vector) is usually called a “3Dtransformation matrix” or more narrowly a “rigid body transform.”

In the particular case of human mandible movement, the possiblemovements are mechanically conditioned to the condyle and fossa, actingas a “ball joint.” This particular condition of “ball joint” movementspermits describing any of those mandible movements (coming from thedifferent poses) as a unique pure rotation (without translation) insteadof the combination of a rotation plus a translation (as any genericmovement requires). FIG. 6 illustrates a method for converting atranslation vector plus the rotation component to a pure rotation arounda unique axis in this particular “ball joint” movement of the condyle inthe fossa.

The scans and poses illustrated in FIGS. 4 and 5, along with theregistration of the pose scans with a reference scan, provides for atranslation vector 40 between start point 41 (origin of coordinates ofmandible 3D object) and 42 (end point of that initial point of themandible), and a rotation vector 46 component referred to as theoriginal rotation axis. The translation vector 40 with the rotationvector 46 is equivalent to a pure rotation axis 47 passing through acomputed point 44. In this way, the movement from the original pose toany given pose that was originally described as the combination of arotation (angle 45) around axis 46 and a translation through translationvector 40 (from point 41 to point 42) NOW can be described as a uniquepure rotation (rotation angle 45) around axis 47. This transformation isperformed to convert the translation vectors and original rotation axesfor each of the mandible positions (open, right, left, forward) to purerotation axes for each of those positions, and the combined movement ofa mandible around those four pure rotation axes provides the virtualarticulation model, as illustrated in FIG. 7. In particular, thisvirtual articulation model uses the pure rotation axes illustrated inFIG. 7 to simulate the comprehensive mandibular movement as acombination of four simple mandibular motions between the bite posescans as follows: open to closed; protrusive or forward to closed;lateral right forward to closed; and lateral left forward to closed.

Input Scans

The input data for generating a virtual articulation model includesseven intra-oral scans: a scan of the maxillary arch as illustrated inFIG. 8; a scan of the mandibular arch as illustrated in FIG. 9; a scanof the closed (centric, maximum inter-cuspidation) bite pose asillustrated in FIG. 10; a scan of the open bite pose, including anintermediary object to maintain the spatial relationship between thearches as illustrated in FIG. 11; a scan of the protrusive (forward)bite pose as illustrated in FIG. 12; a scan of the left lateral bitepose as illustrated in FIG. 13; and a scan of the right lateral bitepose as illustrated in FIG. 14. The digital 3D models or scans in FIGS.8-14 can be obtained using an intra-oral scanner as described above andare illustrative of such input scans from the same patient. These scanscan also possibly be obtained from a library of scans of a patient, orby scanning impressions or castings of the patient's teeth. The inputscans preferably include the full arches but could possibly include onlypartial arches. The bite pose scans can include scans of extreme biteposes to the limits of such movement or, alternatively, scans of biteposes with significant displacement but not to the limit. In the lateralposes, the working side condyle must be in the rear position, rotatingas a “ball joint” without any translation. The other condyle will betranslated forward, but the scan should be done without any overallprotrusion of the mandible. Scanning with the working side condyle inrotation only enables accurate motion representation by the purerotation model.

Calculating Best Fit Registrations and Transforms

The individual mandibular and maxillary arch scans are registered witheach of the bite pose scans. Registration includes finding the bestgeometric fit of the arch scan (mandibular or maxillary) with a bitescan and is an application of known algorithms for registration of twoor more 3D models. For example, one approach for registering 3D data isa known algorithm called Iterative-Closest Point (ICP) matching. Otherregistration algorithms are disclosed in U.S. Patent ApplicationPublication No. 2016/0004811, which is incorporated herein by referenceas if fully set forth.

Registration of the two arches with a bite scan enables computing a 3Dtransform defining the spatial relationship between the two arch scansin the pose of that bite scan. The maxilla is considered fixed in adefault coordinate space. The mandible and maxilla are considered to berigid objects that can move in space but cannot change size. Each biteregistration transform therefore describes the relative translation(position) and rotation (orientation) of the mandible to the maxilla.

Bite registrations are found for the bite scans described above. Thetransformation matrix is found for the mandible in the following poses:open pose as illustrated in FIG. 15; protrusive pose as illustrated inFIG. 16; left lateral pose as illustrated in FIG. 17; and right lateralpose as illustrated in FIG. 18. These bite scans of these poses, shownin FIGS. 15-18, are registered with the closed bite pose scan in thisexample or with a different scan as the reference scan.

Each transformation can be expressed as a 3D matrix containing therotation and translation of the mandible relative to the maxilla withthe rotation expressed as three rotations around the three coordinateaxes (X, Y, and Z), a.k.a. Euler angles. Other equivalent expressionsexist such as an axis-angle rotation plus a translation vector, or aquaternion rotation plus a translation vector. The transforms can bestored in a database, for example, with the rotation stored as a 3×3submatrix and the translation stored as three elements of a column inthe matrix. These transforms are then used to determine thecorresponding pure rotation axes.

In some embodiments for the registration, the maxillary arch can becomprised of any recognizable portion of the maxillary dental arch,maxillary alveolar process, palate, skull, or head, excluding themandible. In particular, the calculated pure rotation axes can bephysically linked to the temporomandibular joint (rear of fossa andupper eminentia angle) morphology. As a result, the virtual articulationobtained at a given time can be re-called at any further time for thesame patient by registering a time-fix part of the oral cavity (thepalate). When registering the palate in a new scan with the palate of aprevious scan for the same patient and which contains the virtualarticulation information, these calculated pure rotation axes will beaccurately transferred to the new scan. A patient's virtual articulationinformation can thus be transferred from one scan to another for thepatient.

Equivalent Pose and Interpolation Representations

Once the registration transforms are known, interpolations between theclosed pose and other individual bite poses can be used to move themandible. Rigid transforms are typically decomposed into rotation andtranslation components that are interpolated separately, then recombinedinto an interpolated transform. Numerous types of interpolations arepossible. Linear interpolation of the two components would result in astraight path through space with an accompanying rotation. Higher orderinterpolations or table based interpolations could be used to modelphysically derived motion paths. The method described herein uses analternate representation of the pose transforms that uses only arotation component to effect the motion, which when interpolated followsa circular arc through space instead of a straight line. This alternaterepresentation more closely approximates the swivel behavior of naturaljaw motion. This representation is referred to as a “pure rotation” andprovides for an equivalent or corresponding rotation to a transformcontaining both translation and rotation, since the pure rotationresults in the same end pose.

Described below are the calculations required for finding thisequivalent or corresponding pure rotation representation. First themethod finds the pure rotation axis and the rotation angle, then itfinds one point of the pure rotation axis to determine the pure rotationaxis position such that the pure rotation attains the desired end posewithout an additional translation.

Finding the original rotation axis and rotation angle involves thefollowing. Rigid body motion can be described as an orientation (3×3rotation matrix, which represents the rotation around the threecoordinate axes) plus a translation (translation vector which representsa vector starting at the coordinate space origin and ending at theequivalent point).

Let R be the 3×3 rotation matrix of a given motion, with its componentslabeled as:

$R = \begin{bmatrix}n_{x} & o_{x} & a_{x} \\n_{y} & o_{y} & a_{y} \\n_{z} & o_{z} & a_{z}\end{bmatrix}$

The rotation angle is calculated as

$\tan^{- 1}\frac{\sqrt{\left( {o_{z} - a_{y}} \right)^{2} + \left( {a_{x} - n_{z}} \right)^{2} + \left( {n_{y} - o_{x}} \right)^{2}}}{n_{x} + o_{y} + a_{z} - 1}$

The original rotation axis is calculated as:

$r_{x} = \frac{o_{z} - a_{y}}{2{\sin (\varnothing)}}$$r_{y} = \frac{a_{x} - n_{z}}{2{\sin (\varnothing)}}$$r_{z} = \frac{n_{y} - o_{x}}{2{\sin (\varnothing)}}$

Finding a point on the pure rotation axis involves the following. A purerotation requires defining the line equation of the pure rotation axisincluding its position. The geometry above produces an original rotationaxis that passes through the coordinate space origin, changing theorientation of the object being transformed but ignoring thetranslational component of the original transform. The desired purerotation requires a pure rotation axis parallel to the original rotationaxis at some offset such that rotation around the pure axis, without atranslation operation, will achieve the same result as the originaltransform (including the translation component).

FIG. 19 represents the coordinate system (X, Y, Z) and the originalrotation axis obtained in the previous section. FIG. 20 shows theoriginal coordinate system, the transformed mandible and the translationvector obtained in the previous section. From the vectorial perspective,the situation is illustrated in FIG. 21.

A key to finding one point of the pure rotation axis is taking intoaccount the following conditions. The pure rotation axis will beparallel to the original rotation axis that passes through the origin.Defining a line (named Auxiliary Line in FIGS. 22-24) starting at themidpoint of the translation vector and perpendicular to it, willintersect the pure rotation axis. The angle rotated to meet thatAuxiliary Line will be half of the rotated angle. By definition, theoriginal rotation axis will always be perpendicular to the translationvector. This vectorial composition is illustrated in FIG. 22.

The pure rotation axis, identified as Pure Rotation Axis in FIGS. 22-24,will intersect the Auxiliary Line at point R. The distance “d” (fromorigin to point R) will be exactly the rotation radius from the origin.The angle between line d and the Auxiliary Line will be half of the purerotation angle calculated before (considering that the Auxiliary Linewas built starting at the middle of the translation vector). For anotherillustration of the vectors, lines, and points involved, see FIGS. 23and 24 including the objects (original and moved) from differentperspectives.

According to this situation, the equations are:

Point R: (X_(R), Y_(R), Z_(R))Point P: (X_(P), Y_(P), Z_(P))Point P₀ (midpoint of translation vector): (X₀, Y₀, Z₀), defined as

$X_{0} = \frac{X_{P}}{2}$ $Y_{0} = \frac{Y_{P}}{2}$$Z_{0} = \frac{Z_{P}}{2}$

u₁ (unitary vector in the direction of the Auxiliary Line): (u_(1x),u_(1y), u_(1z))Rotation angle: φThe parameter u₁ is obtained as the normalized vector product betweenthe translation vector and original rotation axis (both of themavailable from the previous step).

The Auxiliary Line equation could be written as:

X _(R) +X ₀ +λu _(1x)

Y _(R) +Y ₀ +λu _(1y)

Z _(R) +Z ₀ +λu _(1z)

Applying basic trigonometry (where O is the origin point):

$\frac{\overset{\_}{{OP}_{0}}}{d} = {\sin \frac{\varphi}{2}}$

So the rotation radius can be expressed as:

$\begin{matrix}{d = \frac{\overset{\_}{{OP}_{0}}}{\sin \frac{\varphi}{2}}} & (1)\end{matrix}$

But distance “d” can be expressed as well based on the points O and R asfollows:

d ² =X _(R) ² +Y _(R) ² +Z _(R) ²=(X ₀ +λu _(1x))²+(Y ₀ +λu _(1y))²+(Z ₀+λu _(1z))²=(u _(1x) ² +u _(1y) ² +u _(1z) ²)λ²+2(X ₀ u _(2x) +Y ₀ u_(2y) +Z ₀ u _(2z))λ+(X ₀ ² +Y ₀ ² +Z ₀ ²)   (2)

But,

u_(1x) ²+u_(1y) ²+u_(1z) ²=1, provided u₁ is a unitary vectorX₀u_(1x)+Y₀u_(1y)+Z₀u_(1z) is the dot product {right arrow over(OP₀)}·{right arrow over (u₁)} and is equal to 0, provided {right arrowover (OP₀)} is normal to {right arrow over (u₁)}

X ₀ ² +Y ₀ ² +Z ₀ ²= OP ₀ ²

So combining equations (1) and (2), the following is an equation fordetermining λ:

${{\lambda^{2} + {\overset{\_}{{OP}_{0}}}^{2} - \left( \frac{\overset{\_}{{OP}_{0}}}{\sin \frac{\varphi}{2}} \right)^{2}} = {0\mspace{14mu} {this}\mspace{14mu} {is}}},{\lambda^{2} = \frac{{\overset{\_}{{OP}_{0}}}^{2}}{\left( {\tan \frac{\varphi}{2}} \right)^{2}}}$

So, finally, the method obtains the value of λ that determines the pointR on the pure rotation axis as:

$\begin{matrix}{\lambda = \frac{\overset{\_}{{OP}_{0}}}{\tan \frac{\varphi}{2}}}\end{matrix}$

Finally, the point R can be expressed as

$X_{R} = {X_{0} + {\frac{\overset{\_}{{OP}_{0}}}{\tan \frac{\varphi}{2}}u_{1x}}}$$Y_{R} = {Y_{0} + {\frac{\overset{\_}{{OP}_{0}}}{\tan \frac{\varphi}{2}}u_{1y}}}$$Z_{R} = {Z_{0} + {\frac{\overset{\_}{{OP}_{0}}}{\tan \frac{\varphi}{2}}u_{1z}}}$

This procedure is repeated to obtain a rotation point for each of thepure rotation axes of the four poses. The pure rotation axes obtainedfrom this procedure for the four different axes which animate themandible model are represented in FIG. 25. The rotation points andcorresponding rotation angles for the four pure rotation axes can bestored in a database, for example.

Composite Motion Via Combining and Constraining Individual Transforms

The full range of motion of the mandible can be composed from theindividual transforms at varying states of interpolation. Constraining agiven interpolation parameter dependent on the interpolation parametersof other motions can help limit the range of motion to a more faithfulrepresentation of physical reality.

Each of the five bite registrations, by virtue of representing extremeor significant excursions of the jaw, establish constraints of themandibular motion in some directions. For example, the mandible cannotmove more to the left than the extreme left bite pose, nor can themandible close more than the closed bite registration. Therefore,interpolation between (and not extrapolation beyond) the individualextreme poses and the closed pose as an exemplary reference provides oneset of constraints. An example convention for this method is that aninterpolation parameter of 0 represents the closed pose and a parameterof 1 represents a bite pose of one of the other bite scans. Parametersbetween 0 and 1 represent an intermediate pose between the two scannedextremes.

The comprehensive virtual articulation model includes a combination ofthe four interpolated poses which can be expressed as a set of fourinterpolation parameters. An example is shown in the user interface ofFIG. 26 with the displayed sliders (Open, Right, Left, Forward) in thelower right corresponding to the four interpolation parameters. Thisuser interface can be displayed on display device 16. A user can adjustthe displayed sliders using input device 18 (e.g., a cursor-controldevice) to view the corresponding motion of the displayed virtualarticulation model. Adjusting the sliders causes rotation of thecorresponding pure rotation between the two end points for the selectedtype of movement or pose. The sliders also have an animation mode toachieve continuous motion, including multiple sliders animatingsimultaneously with phase differences determined by the user to simulatedifferent complex motion cycles. Aside from sliders, a touch screen canbe used for example, to move the displayed representation of themandibular arch amongst combinations of the four poses.

To constrain the range of motion to match physical reality, additionallimits on the interpolation values can be imposed. For example, the leftand right motions cannot be used simultaneously. This can be expressedas limiting the two respective interpolation parameters so that at mostone of them is non-zero. Rotation values can be restricted to positivevalues—right axis is valid only for lateral right movement; left axis isvalid only for lateral left movement. For combining a lateral rotationwith an open rotation, the open rotation axis must be rotated in thespace according to the lateral rotation. In other words, the open-closehinge must rotate relative to the laterally rotated mandible just asdoes the real human mandible. Additional types of constraints can alsobe utilized. More nuanced physically-based constraints based on humanmotion studies can be added. Collision detection between the archesduring motion can be used to prevent interpenetration between thearches, for example of opposing tooth surfaces.

1. A method for determining virtual articulation from dental scans,comprising steps of: receiving digital 3D models of a person's maxillaryarch and mandibular arch; receiving digital 3D models of a plurality ofdifferent bite poses of the maxillary and mandibular arches; anddetermining a virtual articulation model, based upon the digital 3Dmodels of the plurality of different bite poses, including a purerotation axis of the mandibular arch with respect to the maxillary arch.2. The method of claim 1, wherein the step of receiving digital 3Dmodels of a plurality of different bite poses includes receiving thedigital 3D models for a closed bite pose, an open bite pose, aprotrusive bite pose, a left lateral bite pose, and a right lateral bitepose.
 3. The method of claim 1, wherein the determining step includesregistering the digital 3D models of the maxillary and mandibular archeswith the digital 3D models of the plurality of different bite poses. 4.The method of claim 3, wherein the maxillary arch is comprised of arecognizable portion of the maxillary dental arch, maxillary alveolarprocess, palate, skull, or head, excluding the mandible.
 5. The methodof claim 3, further comprising determining from the registration atransformation matrix containing a rotation submatrix and translationvector for each of the plurality of different bite poses.
 6. The methodof claim 2, wherein the determining step includes determining a purerotation axis relating to the protrusive pose.
 7. The method of claim 2,wherein the determining step includes determining a pure rotation axisrelating to the open pose.
 8. The method of claim 2, wherein thedetermining step includes determining a pure rotation axis relating tothe lateral right pose.
 9. The method of claim 2, wherein thedetermining step includes determining a pure rotation axis relating tothe lateral left pose.
 10. The method of claim 1, further comprisingdisplaying the virtual articulation model on an electronic displaydevice.
 11. A system for determining virtual articulation from dentalscans, comprising: a module for receiving digital 3D models of aperson's maxillary arch and mandibular arch; a module for receivingdigital 3D models of a plurality of different bite poses of themaxillary and mandibular arches; and a module for determining a virtualarticulation model, based upon the digital 3D models of the plurality ofdifferent bite poses, including a pure rotation axis representation foreach bite pose of the mandibular arch with respect to the maxillaryarch.
 12. The system of claim 11, wherein the module for receivingdigital 3D models of a plurality of different bite poses includes amodule for receiving the digital 3D models for a closed bite pose, anopen bite pose, a protrusive bite pose, a left lateral bite pose, and aright lateral bite pose.
 13. The system of claim 11, wherein thedetermining module includes a module for registering the digital 3Dmodels of the maxillary and mandibular arches with the digital 3D modelsof the plurality of different bite poses.
 14. The system of claim 13,wherein the maxillary arch is comprised of a recognizable portion of themaxillary dental arch, maxillary alveolar process, palate, skull, orhead, excluding the mandible.
 15. The system of claim 13, furthercomprising a module for computing from the registration a transformationmatrix containing a rotation submatrix and translation vector for eachof the plurality of different bite poses.
 16. The system of claim 12,wherein the determining module includes a module for determining a purerotation axis relating to the protrusive pose.
 17. The system of claim12, wherein the determining module includes a module for determining apure rotation axis relating to the open pose.
 18. The system of claim12, wherein the determining module includes a module for determining apure rotation axis relating to the lateral right pose.
 19. The system ofclaim 12, wherein the determining module includes a module fordetermining a pure rotation axis relating to the lateral left pose. 20.The system of claim 11, further comprising a module for displaying thevirtual articulation model on an electronic display device.
 21. A methodfor determining and displaying a virtual articulation from dental scans,comprising steps of: receiving digital 3D models of a person's maxillaryarch and mandibular arch; receiving digital 3D models of a plurality ofdifferent bite poses of the maxillary and mandibular arches; determininga virtual articulation model, based upon the digital 3D models of theplurality of different bite poses, including a plurality of purerotation axes of the mandibular arch with respect to the maxillary arch;and displaying a pose of the virtual articulation model on an electronicdisplay device based upon user input for one or more rotations aroundthe pure rotation axes.
 22. The method of claim 21, wherein thedetermining step includes determining pure rotation axes relating to aprotrusive pose, an open pose, a lateral right pose, and a lateral leftpose.